Fed Fix-Up for Fort Hamilton
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Nominations for President
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society September 2013 Volume 60, Number 8 The Calculus Concept Inventory— Measurement of the Effect of Teaching Methodology in Mathematics page 1018 DML-CZ: The Experience of a Medium- Sized Digital Mathematics Library page 1028 Fingerprint Databases for Theorems page 1034 A History of the Arf-Kervaire Invariant Problem page 1040 About the cover: 63 years since ENIAC broke the ice (see page 1113) Solve the differential equation. Solve the differential equation. t ln t dr + r = 7tet dt t ln t dr + r = 7tet dt 7et + C r = 7et + C ln t ✓r = ln t ✓ WHO HAS THE #1 HOMEWORK SYSTEM FOR CALCULUS? THE ANSWER IS IN THE QUESTIONS. When it comes to online calculus, you need a solution that can grade the toughest open-ended questions. And for that there is one answer: WebAssign. WebAssign’s patent pending grading engine can recognize multiple correct answers to the same complex question. Competitive systems, on the other hand, are forced to use multiple choice answers because, well they have no choice. And speaking of choice, only WebAssign supports every major textbook from every major publisher. With new interactive tutorials and videos offered to every student, it’s not hard to see why WebAssign is the perfect answer to your online homework needs. It’s all part of the WebAssign commitment to excellence in education. Learn all about it now at webassign.net/math. 800.955.8275 webassign.net/math WA Calculus Question ad Notices.indd 1 11/29/12 1:06 PM Notices 1051 of the American Mathematical Society September 2013 Communications 1048 WHAT IS…the p-adic Mandelbrot Set? Joseph H. -
The Vile, Dopy, Evil and Odious Game Players
The vile, dopy, evil and odious game players Aviezri S. Fraenkel¤ Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot 76100, Israel February 7, 2010 Wil: We have worked and published jointly, for example on graph focality. Now that one of us is already an octogenarian and the other is only a decade away, let's have some fun; let's play a game. Gert: I'm game. Wil: In the Fall 2009 issue of the MSRI gazette Emissary, Elwyn Berlekamp and Joe Buhler proposed the following puzzle: \Nathan and Peter are playing a game. Nathan always goes ¯rst. The players take turns changing a positive integer to a smaller one and then passing the smaller number back to their op- ponent. On each move, a player may either subtract one from the integer or halve it, rounding down if necessary. Thus, from 28 the legal moves are to 27 or to 14; from 27, the legal moves are to 26 or to 13. The game ends when the integer reaches 0. The player who makes the last move wins. For example, if the starting integer is 15, a legal sequence of moves might be to 7, then 6, then 3, then 2, then 1, and then to 0. (In this sample game one of the players could have played better!) Assuming both Nathan and Peter play according to the best possible strategy, who will win if the starting integer is 1000? 2000?" Let's dub it the Mark game, since it's due to Mark Krusemeyer according to Berlekamp and Buhler. -
TENTH ANNUAL CHARITY DAY SEPTEMBER 11, 2014 • NEW YORK Thursday, September 11, 2014 Marked BGC’S Tenth Annual Charity Day
TENTH ANNUAL CHARITY DAY SEPTEMBER 11, 2014 • NEW YORK Thursday, September 11, 2014 marked BGC’s Tenth Annual Charity Day. BGC Partners, together with its affiliate Cantor Fitzgerald, raised approximately $12 million globally on this single day for dozens of charities around the world. To date, Charity Day has raised approximately $113 million for hundreds of charitable causes. Held in commemoration of the 658 Cantor employees and 61 Eurobrokers employees lost in the 9/11 World Trade Center attacks, each anniversary is a poignant occasion for us. Every year, BGC Partners and our affiliate Cantor Fitzgerald, in conjunction with the Cantor Fitzgerald Relief Fund, strive to turn a tragic day into one that is positive and uplifting by distributing 100% of our global revenues on Charity Day to the Cantor Fitzgerald Relief Fund and dozens of charities around the world. The Cantor Fitzgerald Relief Fund, initially created to assist families of Cantor employees who were lost on 9/11, has since broadened its mission to provide aid to victims of terrorism, natural disasters, emergencies, direct service charities and wounded members of the military. We are thankful to all our celebrity guests who joined us in New York on Charity Day and raised money for tremendous causes. In addition, many thanks to our clients, brokers and charities whose commitment, support, enthusiasm and graciousness made Charity Day a spectacular success. Louis Scotto Executive Managing Director, General Manager, North America BGC Partners, Inc. Miss USA 2012, Nana Meriwether, Front cover: Model, Damaris Lewis, representing the Meriwether Foundation representing the Garden of Dreams Foundation Musician Darryl “DMC” McDaniels, HRH Princess Eugenie of York, representing the Garden of Dreams Foundation representing Children in Crisis Actor, Tony Sirico, Media Personality, Jenny McCarthy, representing Wounded Warrior Project representing Generation Rescue THE CHARITIES AND CAUSES BGC SUPPORTS The mission of Able Community Services, Inc. -
Probability and Random Processes ECS 315
Probability and Random Processes ECS 315 Asst. Prof. Dr. Prapun Suksompong [email protected] 4 Combinatorics Office Hours: BKD, 6th floor of Sirindhralai building Tuesday 9:00-10:00 Wednesday 14:20-15:20 1 Thursday 9:00-10:00 Supplementary References Mathematics of Choice How to count without counting By Ivan Niven permutations, combinations, binomial coefficients, the inclusion-exclusion principle, combinatorial probability, partitions of numbers, generating polynomials, the pigeonhole principle, and much more A Course in Combinatorics By J. H. van Lint and R. M. Wilson 2 Cartesian product The Cartesian product A × B is the set of all ordered pairs where and . Named after René Descartes His best known philosophical statement is “Cogito ergo sum” (French: Je pense, donc je suis; I think, therefore I am) 3 [http://mathemagicalworld.weebly.com/rene-descartes.html] Heads, Bodies and Legs flip-book 4 Heads, Bodies and Legs flip-book (2) 5 Interactive flipbook: Miximal 6 [http://www.fastcodesign.com/3028287/miximal-is-the-new-worlds-cutest-ipad-app] One Hundred Thousand Billion Poems 7 [https://www.youtube.com/watch?v=2NhFoSFNQMQ] One Hundred Thousand Billion Poems Cent mille milliards de poèmes 8 Pokemon Go: Designing how your avatar looks 9 How many chess games are possible? 10 [https://www.youtube.com/watch?v=Km024eldY1A] An Estimate: The Shannon Number 11 [https://www.youtube.com/watch?v=Km024eldY1A] An Estimate: The Shannon Number 12 [https://www.youtube.com/watch?v=Km024eldY1A] An Estimate: The Shannon Number 13 [https://www.youtube.com/watch?v=Km024eldY1A] The Shannon Number: Just an Estimate 14 [https://www.youtube.com/watch?v=Km024eldY1A] Example: Sock It Two Me 15 [Greenes, 1977] Example: Sock It Two Me Jack is so busy that he's always throwing his socks into his top drawer without pairing them. -
Stories That Matter — More Often
Chelsea Clinton on women’s rights. New York City Schools Chancellor Carmen Fari ~n a on successful principals. A special report on the Eric Garner decision. These are just OCTOBER 2015 a few of the extraordinary stories that have aired on MetroFocus, THIRTEEN’s award- winning weekly news and public affairs series. Starting October 19, MetroFocus will air every day on NJTV. That means more stories that matter to you about the issues, people, and events in your own neighborhood and MORE STORIES across the metropolitan region, from New York City, New Jersey, and Connecticut to Long Island, Westchester, and Albany. THAT MATTER — Rafael Pi Roman, Jack Ford, and Jenna Flanigan will host the series, which has been honored with awards from the New York State Broadcasters Association, the Press Club of MORE OFTEN Long Island, and City & State, as well a New York State Emmy Award for Pi Roman. Matt Ryan will be contributing from Albany, and Mary Alice Williams will do the same from Newark. MetroFocus will continue to bring you in-depth reporting, interviews, and solutions-oriented stories on timely topics such as poverty, education, infrastructure, media, healthcare, and more. Celebrities, lawmakers, newsmakers, and other notable New Yorkers will share their favorite metropolitan memories in My MetroFocus segments. Listening In will feature conversations from across the region, while Giving Back will spotlight stories on philanthropy. American Graduate Day segments will keep you up to date on the education champions who inspire students to complete their education and stay on the path to success. “My hope is that MetroFocus becomes appointment viewing WEEKNIGHTS AT 5:30PM for the tri-state audience and becomes known as a ‘go to’ Learn more at JENNA FLANIGAN destination for programming that enlightens, informs, reflects, thirteen.org/metrofocus entertains, and impacts our entire community. -
Meet the Tribute Stars and Their Backing Band…
Meet the tribute stars and their backing band… Sharon Owens (Barbara Streisand): Upon graduating from high school in 1984, Sharon shot off on her way into the real world of touring with American Entertainment Company in Columbus Ohio. A year on the road opening for country acts such as the Mandrells, Letterman, and Willie Nelson, Sharon decided to stop the rolling stone and get her education before returning to the entertainment biz. During her studies, she spent many summers in Cambridge, England, where she studied under John Rutter, the famous 20th century composer. During the school year, Sharon would study Opera during the day then run to her night gig, where she sang and danced in the Busch Gardens Main Theater in Tampa Bay Florida. After years of vocal training and a strong master's of education under her belt, Sharon took off for Los Angeles to pursue a career in ANYTHING that had to do with entertainment. Sharon didn’t realize at the time that she was to become a pioneer in the tribute business. Unlike many of the other impersonators who are “lookalikes,” she didn’t study voice and acting simply to be called a tribute artist. “Imitating Streisand became an acting job,” she insists. “So many movies have been made where famous actors immerse themselves into their movie character and then tell a life story of the REAL person, I simply do the same thing, but on stage.” Soon after starting out as a dynamic mimic of the incomparable Streisand, Sharon began to take the comedy routine more seriously. -
What Comes Next?
NEWSFOCUS For PRESIDENT What Comes Next? arrangement of toothpicks, in which a new batch is added at each stage, centered on and One of mathematicians’ most beloved at right angles to the exposed tips of the pre- e e e e e ic c ic o i ic ic Web sites is getting ready for a makeover. vious batch (see figure). The picture that (Rank candidates o o o o h h h h in order of choice) h C C C C C The Online Encyclopedia of Integer emerges displays surprising fractal growth. t d d h h s n r t t 1 2 3 4 5 Sequences, established by Neil Sloane at “It’s got beautiful structure,” Sloane says. He Candidate A 1 2 3 4 5 AT&T Labs Research in 1996 and run and his AT&T colleague David Applegate largely as a one-man shop, is poised to go have written a paper on the sequence’s math- Candidate B 1 2 3 4 5 “wiki,” with 50 associate editors taking over ematical properties, and Applegate has con- Candidate C 1 2 3 4 5 much of the workload. tributed a movie of its geometric growth, The OEIS, or simply “Sloane” as it’s linked to its entry in the OEIS. Candidate D 1 2 3 4 5 known to sequence fanatics, is a database of Sloane set up the OEIS Foundation last Candidate E 1 2 3 4 5 nearly 200,000 lists of numbers—a mathe- year and transferred intellectual-property matical equivalent to the FBI’s voluminous rights to the nonprofit organization. -
CABINET 48 the FAX NUMBERS of the BEAST, and OTHER MATHEMATICAL SPORTS: an INTERVIEW with NEIL SLOANE Margaret Wertheim
CABINET c US $12 CANADA UK £7US $12 $12 ISSUE 57 A QUARTERLY OF ART AND CULTURE CATASTROPHE 48 THE FAX NUMBERS OF THE BEAST, AND OTHER MATHEMATICAL SPORTS: AN INTERVIEW WITH NEIL SLOANE Margaret Wertheim Everyone knows a few integer sequences: the even networks, which are like artificial brains with com- numbers, the odd numbers, the primes. And we’ve puter simulations of neurons. When these “neurons” all heard about the Fibonacci sequence (1, 1, 2, 3, 5, fire, they trigger other neurons, which in turn trig- 8, 13…), where each term is computed by adding ger others—you have to have a certain amount of together the two previous terms. In 1964, mathema- activity before a neuron gets triggered. And the tician Neil Sloane, then working on a PhD at Cornell question was, “If you have a network of these con- University, began to write down interesting sequences figured in a particular way, and you start by making of numbers on file cards. His research on neural net- one fire, will the activity continue to propagate works generated quite a few; he pressed his friends through the network? Will it die out, or will it satu- for examples and consulted mathematics textbooks. rate the network?” I was looking at models of this, As the horde of sequences grew, he transferred them and I could count the number of cells firing at any to punched cards, then magnetic tape, and eventu- given time, and I would come up with a sequence of ally to the web, where today, more than half a century numbers. -
Commencement Program, 2019
263 rd COMMENCEMENT MAY 20, 2019 20, MAY R D COMMENCEME 263 NT CLA S S O F 2 019 M A Y 20, 20 1 9 CLASS OF 2019 KEEPING FRANKLIN’S PROMISE In the words of one elegiac tribute, “Great men have two lives: one which occurs while they work on this earth; a second which begins at the day of their death and continues as long as their ideas and conceptions remain powerful.” These words befit the great Benjamin Franklin, whose inventions, innovations, ideas, writings, and public works continue to shape our thinking and renew the Republic he helped to create and the institutions he founded, including the University of Pennsylvania. Nowhere does Franklin feel more contemporary, more revolutionary, and more alive than at the University of Pennsylvania. His startling vision of a secular, nonsectarian Academy that would foster an “Inclination join’d with an Ability to serve Mankind, one’s Country, Friends and Family” has never ceased to challenge Penn to redefine the scope and mission of the modern American university. When pursued vigorously and simultaneously, the two missions – developing the inclination to do good and the ability to do well – merge to help form a more perfect university that educates more capable citizens for our democracy. Penn has embodied and advanced Franklin’s revolutionary vision for 279 years. Throughout its history, Penn has extended the frontiers of higher learning and research to produce graduates and scholars whose work has enriched the nation and all of humanity. The modern liberal arts curriculum as we know it can trace its roots to Franklin’s innovation to have Penn students study international commerce and foreign languages. -
40 Years with Sloane's Integer Sequences
40 Years with Sloane’s Integer Sequences Jeffrey Shallit School of Computer Science, University of Waterloo Waterloo, Ontario N2L 3G1, Canada [email protected] http://www.cs.uwaterloo.ca/~shallit 1/1 My Christmas Present in 1974 2/1 Sloane’s First Letter to Me 3/1 Modified Engel expansions Kalpazidou, Knopfmacher, and Knopfmacher (1990) studied expansions of the form 1 1 1 1 1 1 α = a0 + + a1 − a1 + 1 · a2 a1 + 1 · a2 + 1 · a3 −··· for real numbers α, where the ai are non-negative integers with ai positive for i 1. ≥ This expansion is essentially unique provided ai ai . +1 ≥ I tried expanding α = 2/5 and found doubly-exponential growth (a0, a1,...)=(0, 2, 3, 7, 13, 97, 193, 18817, 37633, 708158977,...). Although this particular sequence was not in the OEIS at the time, its even-indexed subsequence (2, 7, 97, 18817, 708158977,...) certainly was (as A002812) and led to the discovery that ... 4/1 Modified Engel expansions 1 2i 2i a i = (2 + √3) + (2 √3) 2 +1 2 − and 2i 2i a i = (2+ √3) + (2 √3) 1. 2 +2 − − From this it was easy to deduce the general form of the expansion for 2/(2r + 1). Compare Aho and Sloane’s 1973 paper, “Some Doubly Exponential Sequences”. Open Problem: find a simple closed form for the expansion of 3/7. 5/1 Some confusing quotients Suppose we set c = a, c = b, and for n 2 define cn to be the 0 1 ≥ smallest integer such that c c n > n−1 . -
Modern Computer Arithmetic (Version 0.5. 1)
Modern Computer Arithmetic Richard P. Brent and Paul Zimmermann Version 0.5.1 arXiv:1004.4710v1 [cs.DS] 27 Apr 2010 Copyright c 2003-2010 Richard P. Brent and Paul Zimmermann This electronic version is distributed under the terms and conditions of the Creative Commons license “Attribution-Noncommercial-No Derivative Works 3.0”. You are free to copy, distribute and transmit this book under the following conditions: Attribution. You must attribute the work in the manner specified • by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Noncommercial. You may not use this work for commercial purposes. • No Derivative Works. You may not alter, transform, or build upon • this work. For any reuse or distribution, you must make clear to others the license terms of this work. The best way to do this is with a link to the web page below. Any of the above conditions can be waived if you get permission from the copyright holder. Nothing in this license impairs or restricts the author’s moral rights. For more information about the license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/ Contents Contents iii Preface ix Acknowledgements xi Notation xiii 1 Integer Arithmetic 1 1.1 RepresentationandNotations . 1 1.2 AdditionandSubtraction . .. 2 1.3 Multiplication . 3 1.3.1 Naive Multiplication . 4 1.3.2 Karatsuba’s Algorithm . 5 1.3.3 Toom-Cook Multiplication . 7 1.3.4 UseoftheFastFourierTransform(FFT) . 8 1.3.5 Unbalanced Multiplication . 9 1.3.6 Squaring.......................... 12 1.3.7 Multiplication by a Constant . -
The Sensual (Quadratic) Form, by John H
The Cams Mathematical Monographs Number Twenty-six (1tt1J.draziv) THE SENSUAL,lORM John H. Conway Princeton University Assisted by Francis YC Fung Published and Distributed by THE MATHEMATICAL ASSOCIATION OF AMERICA © 1997 by The Mathematical Association ofAmerica (Incorporated) Library ofCongress Catalog Card Number 97-74335 Complete Set ISBN 0-88385-000-1 Vol. 26 ISBN 0-88385-030-3 Printed in the United States ofAmerica Current Printing (last digit): 10 9 8 7 6 5 4 3 2 1 THE CARDS MATHEMATICAL MONOGRAPHS Published by THE MATHEMATICAL ASSOCIATION OF AMERICA Committee on Publications James W. Daniel, Chair Carus Mathematical Monographs Editorial Board Steven G. Krantz, Editor Robert Burckel John B. Conway Giuliana P. Davidoff Gerald B. Folland Leonard Gillman The following Monographs have been published: 1. Calculus ofVariations, by G. A. Bliss (out of print) 2. Analytic Functions ofa Complex Variable, by D. R. Curtiss (out of print) 3. Mathematical Statistics, by H. L. Rietz (out of print) 4. Projective Geometry, by J. W. Young (out of print) 5. A History ofMathematics in America before 1900, by D. E. Smith and Jekuthiel Ginsburg (out of print) 6. Fourier Series and Orthogonal Polynomials, by Dunham Jackson (out of print) 7. Vectors and Matrices, by C. C. MacDuffee (out of print) 8. Rings and Ideals, by N. H. McCoy (out of print) 9. The Theory ofAlgebraic Numbers, second edition, by Harry Pollard and Harold G. Diamond 10. The Arithmetic Theory ofQuadratic Forms, by B. W. Jones (out of print) 11. Irrational Numbers, by Ivan Niven 12. Statistical Independence in Probability, Analysis and Number Theory, by Mark Kac 13.